Differential Harnack Estimates for Fisher's Equation
Xiaodong Cao, Bowei Liu, Ian Pendleton, Abigail Ward
TL;DR
This paper derives differential Harnack estimates for Fisher's equation, providing insights into the behavior of solutions, bounds on wave speeds, and classical inequalities.
Contribution
It introduces new differential Harnack estimates for Fisher's equation and applies them to analyze wave speeds and inequalities.
Findings
Lower bounds on traveling wave speeds
New differential Harnack estimates for Fisher's equation
Classical Harnack inequalities constructed
Abstract
In this paper, we derive several differential Harnack estimates (also known as Li-Yau-Hamilton-type estimates) for positive solutions of Fisher's equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions and to construct classical Harnack inequalities.
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